我已经解决了我的问题。我所做的是写在下面：-我的视频模型

public $categories;// i declare a public attribute. 
public function afterSave($insert, $changedAttributes) {
    parent::afterSave($insert, $changedAttributes);
    $this->deleteExistingCategories();
    if (isset($_POST['Video']['categories'])) {
        $this->saveVideoCategories($_POST['Video']['categories']);
    }
}

public function deleteExistingCategories() {
    VideoCategory::deleteAll(['video_id' => $this->video_id]);
}

public function saveVideoCategories($categoriesList) {
  foreach ($categoriesList as $category) {
      $videoCategory = new VideoCategory();
      $videoCategory->video_id = $this->video_id;
      $videoCategory->category_id = $category;
      $videoCategory->save();
  }
}

我的视频格式代码

<ul class="catgss_list">
<?php
$checkedCategories = VideoCategory::findAll(['video_id' => $model->video_id]);
if (isset($checkedCategories)) {
    foreach ($checkedCategories as $selectedCategory) {
        $savedCategories[] = $selectedCategory->category_id;
    }
}
$category = Category::find()->all();
foreach ($category as $cat):
?>
<li>
    <div class="chekbox-lg">
        <label>
            <input type="checkbox" name="Video[categories][]" value="<?php echo $cat->id ?>" 
            <?php
            if (isset($savedCategories)) {
                $isCategory = in_array($cat->id, $savedCategories);
                if (isset($isCategory) && $isCategory == true) {
                    echo "checked";
                }
            }
            ?>
                   >
            <b class="checkmark"></b>
            <span><?php echo $cat->category_name ?></span>
        </label>
    </div>
</li>
<?php endforeach; ?>
</ul>